You can use the F test to verify a claim about a standard deviation (or variance) for 2 data sets. Assumptions: The sample is from a "normal distribution" NOTE: some professors prefer to use the following notation: N~(mean, Standard Deviation) Writing the hypothesis: H0: population standard deviation1 = population standard deviation2 H1: population standard deviation1 is less than, greater than, or not equal to population standard deviation2 Critical Value = shaded area from F table using the degrees of freedom. Degrees of freedom: for numerator (use the info from the bigger Standard Deviation) n-1, for denominator (use the info from the smaller Standard Deviation) n-1. Remember that if the null hypothesis requires two tails, split the alpha before using the tables. Test statistic formula: F = variance1 / variance2 **The bigger variance (standard deviation squared) must be divided by the smaller variance (standard deviation squared).** Calculator: Press STAT Highlight TESTS Select 2-SampFTest Put your information in. **NOTE: S1 must be the biggest standard deviation** Make sure the not equal to, less than, or greater than symbol matches the one in your alternative hypothesis (H1). Highlight Calculate Press ENTER F is the test statistic, and P is the P-value. Rejection of the null hypothesis (Ho): You can reject the null hypothesis if:
Remember: if you are not given an alpha assume you are using 0.05. |
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